1.1 Simple & Compound Interest Formulae

1 FV = PV (1 + i x t)
FV = future value
PV = present value
1 = constant
i = interest rate
t = time (In years)
2 FV = PV (1 + i x t)

1.2 Compounding

Monthly                                                                    12
Annual                                                                      1
Quarterly                                                                  4
Bi-annual/ half yearly/ semi-annual                  2

1.3 Simple interest

1. If you invest R35 000 for 8 years with simple interest being calculated at 9.5% per annum, what is the amount at the end of the period?
FV = PV (1 + i x t)

= R35 000(1 + 9.5% x 8)
= R61 600

Tip: this is a simple interest question because of the wording of the questions. The question is looking at the amount at the end of the period. This is known as the future value.
2. If you borrowed R200 000 for 82 months at 11.05% simple interest per annum, how much will you repay at the end of the period?
FV = PV (1 + i x t)

= R200 000(1 + 11.05% x 82/12)

Tip: this is a simple interest question because of the wording of the questions. The question is looking at the amount at the end of the period. This is known as the future value.

Tip: when the time is in months, convert then into years. This is done by dividing the months given by 12.

3. Calculate the simple interest on R70 000 borrowed for 36 months at 11.8% per annum.
I = PV x i x t
= R70 000 x 11.8% x 36/12

= R24 780

4 What is the principal that must be invested for 2 years at 4 1⁄2% to earn R25 000 simple interest?
PV = I/ (i x t)
= R25 000/ (0.045 x 2)

= R277 777.78

1.4 Simple interest

1. If an investor invests R149 000 for 5 years at an interest rate of 3.5% per annum, what will the value of his investment be at the end of the 5 years if interest is calculated as follows:

Interest compounded half-yearly

FV = PV (1 + i/m) ^mn

= R149 000(1 + 3.5%/2) ^ 20
= R210 801.95

2. An investment will be worth R155 000 if invested for 72 months at a rate of 5.75% per annum, compounded quarterly. What is the present value of the investment?

PV = FV/ (1 = i)^mn
= R155 000/ (1+ 5.75%/4) ^ 24
= R110 044.11

Tip: when time is given in months convert it to years by dividing the given months by 12. m refers
to how many times one is getting interest per year. n refers to the number of years. Note the following value of m:
Quarterly = 4
Monthly = 12
Annually = 1
Half yearly = 2

2.1 Multiplication

The following rules apply:
The product of a positive number and a negative number is a negative number

The product of two negative numbers or two positive numbers is a positive number

2.2 Division

The following rules apply to division:
• The quotient of a positive number and a negative number is a negative number
• The quotient of two negative numbers or two positive numbers is a positive

2.3 Rules of negative numbers

The rules for negative numbers can be summarized as follows:
Addition and subtraction
• Adding a negative number is the same as subtracting a positive
• Subtracting a negative number is the same as adding a positive

2.4 Converting fractions to decimals

To convert a fraction to a decimal number, we divide the numerator of the fraction by the denominator, for example:
1/5 = 0.20

An improper fraction must first be converted to a mixed fraction before it can be converted to a decimal.

2.5 Non-terminating and terminating decimals

A non-terminating decimal never ends. For example:

22/ 7 = 3.1428571….

A terminating decimal is a decimal which is exact and complete. For example:

2/ 5 = 0.40

A recurring decimal
A recurring decimal is in which the last decimal digit is repeated over and over again.

1. Introduction

• The average adult listens with only 25 per cent efficiency
• People spend 70% of their waking hours communicating
• Non-verbal communication accounts for 80% of communication
• Most conflict, misunderstandings and ineffective group performance in the workplace are due to poor communication
• Most occurrences of labour unrest are due to ineffective communication
• The average business person spends between a half and two minutes reading a standard business document

2. The importance of effective communication

• Ensuring accuracy & speed in explaining staff duties
• Developing & maintaining good relationships between employees, management & the public
• Motivating, empowering & consulting with employees
• Persuading employees & clients
• Promoting self-expression

3. The communication process according to Harold Lasswell

Elements of the communication process:

• Sender/ communicator/ transmitter: the person who usually starts the process
• Encoding: the process of the sender transferring a thought into a code of sounds, words, gestures and figures which the receiver will understand
• Message: the information passed on
• Receiver/ respondent/ destination/ audience: the person who gets the message
• Decoding: the interpretation process
• Channel/ medium: how the message is sent from sender to receiver

• Feedback/ reactions: the message the receiver sends back to the sender either verbally or non- verbally

• Noise: the barriers to the process that can prevent correct interpretation of the message

4. Barriers to communication

• Physical barriers: include actual physical noises that confuse or totally prevent a message from being heard.
• Physiological barriers: include hearing or sight disabilities. For example: fatigue after a long shift/flight may impair hearing and vision.
• Psychological barriers: include attitudes and emotions. For example: stress in a difficult situation may impede understanding.
• Semantic barriers: are created when the meaning of actual words used are misunderstood. For example: jargon used
• Intercultural barriers: occur between people of different cultures.

5. Types of effective listening

Attentive listening – you look for the main purpose as quickly as possible & focus on the message
Critical listening – you continuously evaluate & analyse during the conversation
Appreciative listening – you listen, then respond

6. The four elements of list

7. Explicit versus implicit message

Explicit message – precise and clearly expressed
Implicit message – expressed indirectly or not openly conveyed

7. Types of questions

• Open-ended questions – encourage participation, confidence and honesty because they do not elicit a right or wrong answer. Examples, ‘how do you feel about working for a large corporation?’
• Leading questions – are asked in such a way that the interviewer leads the interviewee towards the answer they want. Example, ‘ In my opinion all managers salaries should be performance based- what do you think?’
• Specific questions – are limited to one correct answer. For example, ‘in what year did you finish your degree?’
• Hypothetical questions – put the interviewee in a certain imagined scenarios and ask him or her to respond. For example, ‘if you could improve anything in the reception area of this organisation, what would it be?’
• Closed questions – can be answered with a ‘yes’ or a ‘no’. Example, ‘did your qualification give you the skills you need for the job?’

1. Different ways of reading

• Scanning – rapid reading & looking for specific words without being interest in their meaning
• Skimming – the reader wants to get a general idea of what the writer has written
• Comprehensive reading – involves careful reading to understand the meaning or importance of the communication

2. Précis (summary)

Uses of Précis in the commercial environment:

• Outlining the main features of a report
• Summarising
• Reviewing books, magazines, and articles

3. Indirect written vs. Direct written communication

• Indirect written communication: as it is an article targeting a large impersonal audience via the mass media and no direct feedback is expected. For example: advertisements, press releases and newspaper reports and articles
• Direct written communication implies a personal, one-on-one link between writer and reader and the expectation of direct feedback. For example: letters, faxes, memos and reports.

4. Barriers to written communication

• Unfamiliar language
• Unclear and complicated words
• Attitude of writer and reader (psychological barriers)

5. Things to consider when identifying the main ideas

Three things to consider when identifying the main ideas in both spoken and written communication:

• The topic or gist of article: this is the broad concept being expressed and is often included in the heading.
• The main idea/key concept:is the most important piece of information the writer wants to share.
• The supporting ideas: adds information to the main idea by telling how, what, when, why, how much and
  how many.

1. Types of formal private meetings

• Brainstorming – staff gather to exchange new ideas for a project or project
•  Problem solving – coming together of team members to decide mutually on a solution
• Briefings – people gather to be told about work or tasks
• Consulting – a staff member, director or representative of a company meets with outsider companies, clients, suppliers, the media or government bodies
• Technology driven – more & more popular with companies with world-wide operations

2. Basic terminology for meetings

• Ad hoc committee – committee formed for a specific purpose – dissolved on completion
• Agenda – list of all the topics to be discussed, numbered in a specific order
• Quorum – minimum number of members who must be present for the meeting to process and for decisions taken to be valid
• Notice – information given in advance with the details of the venue, date and time of a meeting
• Honorarium – a voluntary fee allocated to a person in recognition of a service given for a fee

3. Types of meetings

• Private meetings – members of an organisation or people who are invited can attend. Many formal procedures have to be followed and notice is sent out to these attending
• Public meeting – are convened to discuss socio-economic and political issues. Members of the general public can attend and usually no formal voting takes place. Notice of these meetings is usually communicated through mass
  media

4. Documents required for a meeting

Three documents used for meetings:

• Notice – sent to members or interested parties to give them the details of the meeting
• Agenda – the list of things to be done at a particular meeting
• Minutes – the official, unbiased record of what was discussed & decided on in a meeting

5. Duties of chairperson and secretary

Duties and powers of the chairperson or secretary:
Ensure the meeting is properly constituted                                  Chairperson
Announce the results of the voting                                                 Chairperson
Oversee financial matters in the absence of the treasurer         Secretary
Count votes (if no appointed voting officer is present)              Secretary
Circulate the attendance register                                                    Secretary
Summarise arguments for and against motions                          Chairperson